绕中心旋转线 [英] Rotate line around center

问题描述

我必须使用专有的图形引擎来绘制线条.我可以通过其原点 (P1) 旋转整个图形.我想要的是围绕其中心点(M)旋转它.所以基本上它看起来像 L_correct 而不是 L_wrong.

I have to use a propriertary graphics-engine for drawing a line. I can rotate the whole drawing by its origin point (P1). What I want, is to rotate it around its center point(M). So basically that it looks like L_correct instead of L_wrong.

我认为，应该可以通过将其从 P1 移到 P2 来纠正它.但我无法弄清楚可以使用什么公式来确定距离.大概一定涉及到角度、宽度、高度……

I think, it should be possible to correct it, by moving it from P1 to P2. But I cannot figure out what formula could be used, to determine the distance. It must probably involve the angle, width and height...

所以基本上我的问题是，是否有一个函数可以根据我的可用数据确定 x2 和 y2?

So basically my question is, if there is a function to determine x2 and y2 based on my available data?

推荐答案

假设您有一个原始方法，可以将绘图旋转任意给定角度 phi.您想要的是使用该图元围绕点 M 旋转绘图 D.这是如何进行的草图.

Let's assume you have a primitive method that rotates a drawing by any given angle phi. What you want is to use that primitive to rotate a drawing D around a point M instead. Here is a sketch of how to proceed.

1. 通过-M翻译你的画，即，将变换T(P) = P - M应用于所有点P> 在你的画中.让 T(D) 成为 D 的翻译.

1. Translate you drawing by -M, i.e., apply the transformation T(P) = P - M to all points P in your drawing. Let T(D) be the translation of D.

现在使用图元将 T(D) 旋转所需的角度 phi.让 R(T(D)) 成为结果.

Now use the primitive to rotate T(D) by the desired angle phi. Let R(T(D)) be the result.

现在用M翻译之前的结果，得到旋转后的图.换句话说，使用转换T'(P) = P + M.

Now translate the previous result by M and get the rotated drawing. In other words, use the transformation T'(P) = P + M.

请注意，在上面的步骤 1 中，M 被映射到原点 0，已知旋转原语在此处工作.在第 2 步旋转后，第 3 步的相反平移将图形放回其原始位置，因为这次 0 映射到 M.

Note that in step 1 above M is mapped to the origin 0, where the rotation primitive is known to work. After rotating in step 2, the opposite translation of step 3 puts back the drawing on its original location as this time 0 is mapped to M.

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